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the sum of fourth and eight terms of an A.P is 54 and their product is 665. find the sum of the first thirty terms of an A.P​
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Asked by sakshinde95 | 23 Jan, 2023, 05:50: PM
answered-by-expert Expert Answer
Let a be the first term and d be the common difference of A.P
 
Fourth term of A.P = a + 3d
 
Eighth term of A.P. = a + 7d
 
Sum of fourth term and eighth term = 2 a + 10 d = 54
 
Hence , we get , a + 5 d = 27 ........................(1)
 
Product of fourth term and eight term is 665.
 
Hence we have ,  ( a + 3d ) ( a + 7d ) = 665
 
Let us eliminate first term of A.P , i.e. a in above expression  ( 2) using eqn.(1)
 
[ ( 27- 5d )  + 3d ]  [ (27-5d) + 7d ) = 665
 
( 27 - 2d) ( 27 + 2d ) = 665
 
729 - 4 d2 = 665 
 
hence we get d = 4
 
by substituting d in eqn.(1) , we get a = 7
 
sum S of 30 terms is determined from following formula
 
S = (n/2) [ 2 a + (n-1) d ]
 
where n is number of terms.
 
Sum of 30 terms = (30/2) [ 14 + 29 × 4 ] = 1950
 





Answered by Thiyagarajan K | 23 Jan, 2023, 06:32: PM

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the sum of fourth and eight terms of an A.P is 54 and their product is 665. find the sum of the first thirty terms of an A.P​
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Asked by sakshinde95 | 23 Jan, 2023, 05:50: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
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